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Berry-Esseen Type Bounds for Transformations of Chi-Squared Variables and Its Statistical Applications

by Ulyanov, Vladimir V., Christoph, Gerd, Fujikoshi, Yasunori.

Series: 2006-14, Preprints

62H10 Distribution of statistics
62E20 Asymptotic distribution theory

We get computable error bound of order $O(n^{-1})$ for
chi-squared with 1 degree of freedom approximation of
transformed chi-squared random variable with $n$ degrees of
freedom. The result is applied for likelihood ratio statistics
in multivariate case.

Computable error bound, chi-squared approximation, likelihood ratio statistics, transformation of random variables

This paper was published in:
Siberian Mathematical Journal, Vol. 47, No. 6, pp. 1154-1166, 2006